Final answer:
The nurse should disinfect the stethoscope with alcohol swabs after using it on a patient under contact precautions.
Step-by-step explanation:
The appropriate action for a nurse after using a stethoscope on a patient with contact precautions is to disinfect it. This means the correct option is B.) Disinfect it with alcohol swabs. Disinfecting is crucial to prevent the spread of infection and to maintain a safe environment for other patients. It is not necessary to dispose of the stethoscope, as it is not a single-use item. Sterilization in an autoclave is generally reserved for instruments that come into contact with sterile body areas or are used in surgical procedures. Using the stethoscope immediately on another patient without disinfection could lead to cross-contamination and is not advisable.